Methods for high-performance electron microscopy

Abstract

Methods for correcting one or more image aberrations in an electron microscopy image, including cryo-EM images, are provided. The method includes obtaining a plurality of electron microscope (EM) images of an internal reference grid sample having one or more known properties, the plurality of electron microscope images obtained for a plurality of optical conditions and for a plurality of coordinated beam-image shifts. The method may also include, among other features, determining an aberration correction function that predicts aberrations for every point in the imaged area using kernel canonical correlation analysis (KCCA).

What is claimed is: 
     
         1 . A method for correcting one or more image aberrations in an electron microscopy image, the method comprising:
 (a) obtaining a plurality of electron microscope (EM) images of an internal reference grid sample having one or more known properties, the plurality of electron microscope images obtained for a plurality of optical conditions and for a plurality of coordinated beam-image shifts, wherein the plurality of optical conditions is selected from a plurality of defocuses, a plurality of z-heights, a plurality of beam tilts, a plurality of beam parallelizations, and any combination thereof;   (b) correcting the plurality of EM images for sample drift by aligning and motion-correcting the plurality of EM images to produce an EM micrograph;   (c) calculating the Fourier transform (FT) of the micrograph to produce an FT image;   (d) deconvolving the FT image using one or more predetermined deconvolution coefficients selected from a range of deconvolution coefficients values to produce a deconvolved FT image;   (e) applying a high-pass filter to the deconvolved FT image to produce a filtered deconvolved FT image;   (f) calculating an inverse FT of the filtered deconvolved FT image to produce an aberration-corrected EM micrograph;   (g) determining an intensity distribution for the aberration-corrected EM micrograph;   (h) calculating a moment for the intensity distribution; and   (i) repeating (c)-(h) using one or more predetermined deconvolution coefficients selected from the range of deconvolution coefficients values that is different than the previous iteration until an optimal one or more deconvolution coefficients is determined based on maximization of the moment in (i).   
     
     
         2 . The method according to  claim 1 , further comprising:
 (j) determining an aberration correction function that predicts aberrations for every point in the imaged area using kernel canonical correlation analysis (KCCA) of the optimal one or more deconvolution coefficients obtained in (i) and the plurality of optical conditions and plurality of coordinated beam-image shifts used in (a).   
     
     
         3 . The method according to  claim 2 , further comprising:
 (k) obtaining one or more EM images of a calibration check grid sample having one or more known properties that is different than at least one of the one or more known properties of the internal reference grid sample;   (l) applying the aberration correction function to the one or more EM images obtained in (k) to produce an aberration corrected EM image; and   (m) determining suitability of the aberration correction function based on comparison of one or more features in the aberration corrected EM image corresponding to one or more known properties of the calibration check grid sample.   
     
     
         4 . The method according to  claim 1 , wherein the internal reference grid sample comprises an amorphous material distributed over a support, wherein the amorphous material comprises a thickness of five or fewer atomic layers and has an atomic mass heavier than the material comprising the support. 
     
     
         5 . The method according to  claim 4 , wherein the amorphous material comprises a metal. 
     
     
         6 . The method according to  claim 5 , wherein the amorphous material has a thickness of one atomic layer. 
     
     
         7 . The method according to  claim 5 , wherein the metal is selected from the group consisting of gold, platinum, iridium, palladium, and any combination thereof. 
     
     
         8 . The method according to  claim 4 , wherein the support comprises a crystalline support having known unit cell dimensions. 
     
     
         9 . The method according to  claim 4 , wherein the support comprises a crystalline support comprising a material selected from the group consisting of graphene, graphene oxide, silicon, and silicon nitride. 
     
     
         10 . The method according to  claim 1 , wherein the one or more known properties is selected from the group consisting of atomicity of the support and unit cell dimensions of the support. 
     
     
         11 . The method according to  claim 1 , wherein the one or more image aberrations comprises monochromatic aberrations affecting phase and amplitude of the Fourier transform of the image. 
     
     
         12 . The method according to  claim 1 , wherein the one or more image aberrations is selected from the group consisting of geometrical distortion, curvature of the image field, and any combination thereof. 
     
     
         13 . The method according to  claim 1 , wherein the one or more image aberrations is selected from the group consisting of constant phase offset, image displacement, defocus, twofold astigmatism, axial coma, threefold astigmatism (trefoil), spherical aberration, star aberration, fourfold astigmatism, 5 th -order axial coma, three-lobe aberration, fivefold astigmatism, 6 th -order spherical aberration, 6 th -order star aberration, rosette aberration, and sixfold astigmatism. 
     
     
         14 . The method according to  claim 1 , wherein the high-pass filter removes all frequencies lower than 1/50 Å. 
     
     
         15 . The method according to  claim 1 , wherein the high-pass filter removes all frequencies lower than 1/500 Å. 
     
     
         16 . The method according to  claim 1 , wherein calculating a moment comprises quantifying the shape of the intensity distribution based on a function that is suitable for optimization with independent component analysis (ICA). 
     
     
         17 . The method according to  claim 16 , wherein the function is selected from the group consisting of negative entropy, skewness, and kurtosis. 
     
     
         18 . The method according to  claim 1 , wherein calculating a moment comprises quantifying the shape of the intensity distribution based on optimizing negative entropy. 
     
     
         19 . The method according to  claim 1 , wherein the plurality of EM images are obtained at a plurality of magnifications. 
     
     
         20 . The method according to  claim 2 , wherein the KCCA is run hierarchically to correct for a time-variable component of one or more aberrations. 
     
     
         21 . A method for correcting geometrical distortion in an electron microscopy image, the method comprising:
 (a) obtaining a plurality of electron microscope (EM) images of an internal reference grid sample having one or more known properties, the plurality of electron microscope images obtained for a plurality of optical conditions and for a plurality of coordinated beam-image shifts, wherein the plurality of optical conditions is selected from a plurality of defocuses, a plurality of z-heights, a plurality of beam tilts, and any combination thereof;
 wherein the internal reference grid sample comprises an amorphous material distributed over a crystalline support having known unit cell dimensions, the amorphous material comprising a thickness of five or fewer atomic layers. 
   (b) correcting the plurality of EM images for sample drift by aligning and motion-correcting the plurality of EM images to produce an EM micrograph;   (c) calculating the Fourier transform (FT) of the micrograph to produce an FT image;   (d) identifying diffraction peaks on the FT image corresponding to the crystalline lattice of the internal reference grid sample;   (e) performing dual space filtering on the FT image by masking the identified diffraction peaks thereby keeping only the diffraction peaks and their corresponding intensities while discarding all information between the diffraction peaks to produce a filtered FT image;   (f) calculating an inverse FT of the filtered FT image to produce a filtered EM micrograph;   (g) selecting a portion of the filtered EM micrograph, calculating a FT image corresponding to the portion to produce a FT sub-image, identifying a subgroup of diffraction peaks on the FT sub-image, indexing diffraction maxima for the subgroup of diffraction peaks, and determining unit cell parameters for the subgroup of diffraction peaks;   (h) determine, using a deformation matrix, whether the one or more unit cell parameters determined in (g) are consistent with the known unit cell dimensions of the crystalline support of the internal reference grid sample; and   (i) calculate a metric tensor based on the deformation matrix.   
     
     
         22 . The method according to  claim 21 , further comprising:
 (j) determining an aberration correction function that predicts the geometric distortion for every point in the imaged area using kernel canonical correlation analysis (KCCA) of the metric tensor obtained in (i) and the plurality of optical conditions and beam-image shifts used in (a).   
     
     
         23 . The method according to  claim 22 , further comprising:
 (k) obtaining one or more EM images of a calibration check grid sample having one or more known properties that is different than at least one of the one or more known properties of the internal reference grid sample;   (l) applying the aberration correction function to the one or more EM images obtained in (l) to produce an aberration corrected EM image   (m) determining suitability of the aberration correction function based on comparison of one or more features in the aberration corrected EM image corresponding to one or more known properties of the calibration check grid sample.   
     
     
         24 . The method according to  claim 21 , wherein the amorphous material comprises a metal. 
     
     
         25 . The method according to  claim 24 , wherein the amorphous material has a thickness of one atomic layer. 
     
     
         26 . The method according to  claim 25 , wherein the metal is selected from the group consisting of gold, platinum, iridium, palladium, and any combination thereof. 
     
     
         27 . The method according to  claim 21 , wherein the support comprises a crystalline support comprising a material selected from the group consisting of graphene, graphene oxide, silicon, and silicon nitride. 
     
     
         28 . The method according to  claim 21 , wherein the plurality of EM images are obtained at a plurality of magnifications. 
     
     
         29 . The method according to  claim 21 , wherein the plurality of EM images are obtained without changing the grid sample position. 
     
     
         30 . The method according to  claim 21 , wherein the KCCA is run hierarchically to correct for a time-variable component of one or more aberrations. 
     
     
         31 . The method according to  claim 21 , further comprising transforming, based on the deformation matrix in (i), all aberrations affecting phase to a Cartesian coordinate system.